As per your request, I am giving you list of the institute in Kerala offering the Ph.D degree.

Cochin University of Science and Technology,
Kochi
Doctorate in Philosophy

Amrita Institute of Medical Sciences,
Kerala – Other
PhD in Pharmaceutical Sciences - 5 Years , Full Time , Doctorate Degree

Indian Institute Of Space Science & Technology,
Thiruvananthapuram
Doctorate in Philosophy - 5 Years , Full Time , Doctorate Degree

University of Kerala,
Thiruvananthapuram
Ph. D. in Aquatic Biology and Fisheries - Full Time , Doctorate Degree

Model Engineering College,
Kochi
PhD in Electronics and communication - 2 Years , Full Time , Doctorate Degree

Rajiv Gandhi Centre for Biotechnology,
Kerala – Other
PhD In Animal Biotechnology - 3 Years , Full Time , Doctorate Degree

Centre for Development Studies (CDS) –
Kerala, Thiruvananthapuram
PhD (Economics) - 5 Years , Full Time , Post Graduate Degree